One of the points of intersection of the curves y=1+3 x-2 x^2 and y=1/x is (1/2, 2). Let the area of the region enclosed by these curves be 1/24(l √…

One of the points of intersection of the curves $\displaystyle y=1+3 x-2 x^2$ and $\displaystyle y=\frac{1}{x}$ is $\displaystyle \left(\frac{1}{2}, 2\right)$. Let the area of the region enclosed by these curves be $\displaystyle \frac{1}{24}(l \sqrt{5}+m)-n \log _{\mathrm{e}}(1+\sqrt{5})$, where $\displaystyle l, m, n \in \mathbf{N}$. Then $\displaystyle l+\mathrm{m}+\mathrm{n}$ is equal to